[Paper Review] Probing the $R_{K^{(*)}}$ Anomaly at a Muon Collider

Guoyuan Huang, Sudip Jana+2 more|arXiv (Cornell University)|Mar 2, 2021

Particle physics theoretical and experimental studies87 references4 citations

TL;DR

This paper proposes using a high-energy muon collider to probe the $R_{K^{(*)}}$ anomaly in $B$-physics via the $\mu^+\mu^- \to b\bar{s}$ process, testing $Z^\prime$ bosons and leptoquark models. With $\sqrt{s} = 6$ TeV and $4\ \text{ab}^{-1}$ luminosity, the setup can cover the full $2\sigma$ parameter space favored by global fits to $R_{K^{(*)}}$ data, including both $s$-channel $Z^\prime$ and $t$-channel leptoquark scenarios.

ABSTRACT

The LHCb measurements of the $\ensuremath{\mu}/e$ ratio in $B\ensuremath{ ightarrow}K\ensuremath{\ell}\ensuremath{\ell}$ decays $({R}_{K})$ indicate a deficit with respect to the Standard Model prediction, supporting earlier hints of lepton universality violation observed in the ${R}_{{K}^{(*)}}$ ratio. Possible explanations of these $B$-physics anomalies include heavy ${Z}^{\ensuremath{'}}$ bosons or scalar and vector leptoquarks mediating $b\ensuremath{ ightarrow}s{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. We note that a muon collider can directly measure this process via ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{ ightarrow}b\overline{s}$ and can shed light on the lepton nonuniversality scenario. Investigating currently discussed center-of-mass energies $\sqrt{s}=3$, 6 and 10 TeV, we show that the parameter space of ${Z}^{\ensuremath{'}}$ and leptoquark solutions to the ${R}_{{K}^{(*)}}$ anomalies can be mostly covered. Effective operators explaining the anomalies can be probed with the muon collider setup $\sqrt{s}=6 ext{ } ext{ }\mathrm{TeV}$ and integrated luminosity $L=4 ext{ } ext{ }{\mathrm{ab}}^{\ensuremath{-}1}$.

Motivation & Objective

• To test the $R_{K^{(*)}}$ anomaly—indicating lepton universality violation in $b \to s \mu^+ \mu^-$ transitions—using a future muon collider.
• To evaluate the sensitivity of muon collider experiments to $Z^\prime$ bosons and scalar/vector leptoquarks as solutions to the $R_{K^{(*)}}$ anomaly.
• To determine whether the $\mu^+\mu^- \to b\bar{s}$ process can probe the effective operator structure underlying the anomaly.
• To assess the impact of flavor tagging and di-jet SM backgrounds on signal detection at different center-of-mass energies.
• To establish the required collider energy and luminosity to cover the $2\sigma$ favored parameter space from global $B$-physics fits.

Proposed method

• Modeling the $R_{K^{(*)}}$ anomaly via $Z^\prime$ bosons (s-channel) and scalar/vector leptoquarks (t-channel), with effective Lagrangians for $b\bar{s}\mu^+\mu^-$ couplings.
• Computing the $\mu^+\mu^- \to b\bar{s}$ cross section at $\sqrt{s} = 3$, 6, and 10 TeV, including $t$-channel and $s$-channel contributions.
• Evaluating signal-to-background ratios by comparing leptoquark signals to SM di-jet backgrounds, with and without flavor tagging.
• Using effective field theory to describe high-mass leptoquarks ($M_{S_3} = 30$ TeV) as integrated-out particles, leading to effective operators with coefficients $C_9^\mu$ and $C_{10}^\mu$.
• Performing a $3\sigma$ sensitivity analysis on $|C_9^\mu|^2 + |C_{10}^\mu|^2$ as a function of $\sqrt{s}$, assuming $L = 4\ \text{ab}^{-1} \cdot [\sqrt{s}/(6\ \text{TeV})]^2$.
• Comparing results to existing LHC limits and HL-LHC projections for high-energy dimuon tails.

Experimental results

Research questions

• RQ1 Can a muon collider at $\sqrt{s} = 6$ TeV and $L = 4\ \text{ab}^{-1}$ probe the full $2\sigma$ parameter space of $Z^\prime$ and leptoquark models explaining the $R_{K^{(*)}}$ anomaly?
• RQ2 How does flavor tagging affect the sensitivity to $\mu^+\mu^- \to b\bar{s}$ beyond SM di-jet backgrounds?
• RQ3 To what extent do $t$-channel leptoquark exchanges enhance the cross section compared to $s$-channel $Z^\prime$ contributions?
• RQ4 What is the sensitivity of the muon collider to effective operators $C_9^\mu$ and $C_{10}^\mu$ in the $b\to s\mu^+\mu^-$ transition?
• RQ5 How do the results compare to existing LHC constraints and future HL-LHC projections for $bs\mu\mu$ couplings?

Key findings

• At $\sqrt{s} = 6$ TeV and $L = 4\ \text{ab}^{-1}$, the muon collider can probe the full $2\sigma$ favored region of $C_9^\mu = -C_{10}^\mu \in [0.29, 0.57]$ from global $B$-physics fits.
• The best-fit point $C_9^\mu = -C_{10}^\mu = -0.43$ is reachable without flavor tagging, and the entire $2\sigma$ range is covered with flavor tagging at $\sqrt{s} \gtrsim 6$ TeV.
• For vector leptoquarks, $t$-channel enhancement at low $Q^2$ increases sensitivity at small masses, while scalar leptoquarks lack such enhancement due to chirality reversal.
• When the leptoquark mass is $M_{S_3} = 30$ TeV, the signal-to-background ratio becomes nearly constant, indicating decoupling and effective operator dominance.
• The $\mu^+\mu^- \to b\bar{s}$ process at $\sqrt{s} = 6$ TeV can probe $Z^\prime$ and leptoquark models that explain the $R_{K^{(*)}}$ anomaly with high statistical significance.
• The setup with $\sqrt{s} = 6$ TeV and $L = 4\ \text{ab}^{-1}$ outperforms existing LHC limits and HL-LHC projections for $bs\mu\mu$ couplings in the relevant energy range.